Which quantity measures the area of a sector of a circle?

Which quantity measures the area of a sector of a circle?

• A. Arc length
• B. Sector Area
• C. Sine
• D. Radius

Answer: (B)

The size of a sector is described by its area—the amount of space inside the wedge formed by two radii and the arc. This sector area grows with both how far the circle extends (the radius) and how wide the sector is (the central angle). The quantity that captures this is the sector area. When the central angle is in radians, the area is A = (1/2) r^2 θ. If you know the angle in degrees, you can use A = (θ/360) π r^2. This shows the dependence on both radius and angle. Arc length, by contrast, measures along the curved edge, not the enclosed area. Sine is a trigonometric ratio, not an area measure for a circular sector. Radius is a linear distance, not an area.

The size of a sector is described by its area—the amount of space inside the wedge formed by two radii and the arc. This sector area grows with both how far the circle extends (the radius) and how wide the sector is (the central angle). The quantity that captures this is the sector area.

When the central angle is in radians, the area is A = (1/2) r^2 θ. If you know the angle in degrees, you can use A = (θ/360) π r^2. This shows the dependence on both radius and angle.

Arc length, by contrast, measures along the curved edge, not the enclosed area. Sine is a trigonometric ratio, not an area measure for a circular sector. Radius is a linear distance, not an area.